BBC
Defence Secretary Leon Panetta has spoken to South Korea's Kim Kwan-jin, while the US Secretary of State met her Japanese counterpart in Washington.
They called for a peaceful and stable transition of power in North Korea.
Kim Jong-il died on Saturday of a heart attack. His death was announced early on Monday by state media.
The 69-year-old had been in the process of formalising his third son, Kim Jong-un, as his successor.
But the transition had not been completed and analysts fear Mr Kim's death could triggered a period of instability in the internationally isolated nuclear-armed state.
Inside North Korea, citizens appear to be mourning Mr Kim - their leader since the death of his father Kim Il-sung in 1994.
In a telephone conversation early on Tuesday, the US and South Korean defence ministers agreed to co-ordinate closely and maintain a "strong defence posture", Yonhap news agency reported.
The two countries' presidents also spoke shortly after the death was announced.
South Korea's military has been put on alert. The government has also increased its alert level against possible cyber attacks from North Korea.
Chinese condolences
Secretary of State Hillary Clinton held talks with Japanese Foreign Minister Koichiro Gemba, in Washington for a pre-arranged visit.
"We both share a common interest in a peaceful and stable transition in North Korea as well as ensuring regional peace and stability," Mrs Clinton said.
"We reiterate our hope for improved relations with the people of North Korea and remain deeply concerned about their well-being."
A White House spokesman said it was too early to assess what impact a new leader might have in the communist state.
Japan's top government spokesman said Japan, South Korea and the US were considering holding high-level talks on the situation "at the soonest possible opportunity".
Chinese President Hu Jintao, meanwhile, has visited the North Korean embassy in Beijing to offer his condolences, China's Xinhua news agency said.
Late on Monday, the Chinese foreign minister also met the North Korean envoy in Beijing, the agency reported.
China is North Korea's closest ally and its biggest trading partner.
It is keen to avoid a power struggle that could bring further instability to the region or any kind of collapse that would send a tide of North Korean refugees across its border.
In a statement on Monday, Beijing called on North Koreans to unite under the leadership of Kim Jong-un.
Kim Jong-un, hailed by North Korean media as the "Great Successor", is believed to have visited China on at least one occasion in recent months.
Not much is known about the younger Kim, who is thought to be in his late twenties. He was first introduced in public as Kim Jong-il's ear-marked successor in September 2010.
In North Korea, a period of official mourning for Kim Jong-il is under way. He is to be buried on 28 December.
Footage from Pyongyang showed North Koreans crying and grieving for the long-time leader.
US Secretary of State Hillary Clinton and her Japanese counterpart Koichiro Gemba held talks in Washington
The United States has been urgently consulting its allies in East Asia following the death of North Korean leader Kim Jong-il.
They called for a peaceful and stable transition of power in North Korea.
Kim Jong-il died on Saturday of a heart attack. His death was announced early on Monday by state media.
The 69-year-old had been in the process of formalising his third son, Kim Jong-un, as his successor.
But the transition had not been completed and analysts fear Mr Kim's death could triggered a period of instability in the internationally isolated nuclear-armed state.
Inside North Korea, citizens appear to be mourning Mr Kim - their leader since the death of his father Kim Il-sung in 1994.
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“Start Quote
Hillary Clinton US Secretary of StateWe reiterate our hope for improved relations with the people of North Korea and remain deeply concerned about their well-being”
But his unexpected death has rattled neighbours.
The two countries' presidents also spoke shortly after the death was announced.
South Korea's military has been put on alert. The government has also increased its alert level against possible cyber attacks from North Korea.
Chinese condolences
Secretary of State Hillary Clinton held talks with Japanese Foreign Minister Koichiro Gemba, in Washington for a pre-arranged visit.
"We both share a common interest in a peaceful and stable transition in North Korea as well as ensuring regional peace and stability," Mrs Clinton said.
"We reiterate our hope for improved relations with the people of North Korea and remain deeply concerned about their well-being."
A White House spokesman said it was too early to assess what impact a new leader might have in the communist state.
Continue reading the main story 
North Korea
- Population about 23 million
- One million-strong army thought to be world's fifth largest
- Manufacturing output mainly geared to military's demands
- All aspects of daily life strictly controlled by government
- Daily food shortages; acute power cuts and poor infrastructure
America would "judge the North Korean government as we always have, by its actions and by its actions with regard in particular to upholding its commitments regarding denuclearisation", Jay Carney said.
Chinese President Hu Jintao, meanwhile, has visited the North Korean embassy in Beijing to offer his condolences, China's Xinhua news agency said.
Late on Monday, the Chinese foreign minister also met the North Korean envoy in Beijing, the agency reported.
China is North Korea's closest ally and its biggest trading partner.
It is keen to avoid a power struggle that could bring further instability to the region or any kind of collapse that would send a tide of North Korean refugees across its border.
In a statement on Monday, Beijing called on North Koreans to unite under the leadership of Kim Jong-un.
Kim Jong-un, hailed by North Korean media as the "Great Successor", is believed to have visited China on at least one occasion in recent months.
Not much is known about the younger Kim, who is thought to be in his late twenties. He was first introduced in public as Kim Jong-il's ear-marked successor in September 2010.
In North Korea, a period of official mourning for Kim Jong-il is under way. He is to be buried on 28 December.
Footage from Pyongyang showed North Koreans crying and grieving for the long-time leader.
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